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IV. Ecosmomics: Independent, UniVersal, Complex Network Systems and a Genetic Code-Script Source

Cavalcante, Hugo, et al. Predictability and Control of Extreme Events in Complex Systems. arXiv:1301.0244. In this January 2013 posting, systems physicists Cavalcante and Marcos Oria, Universidade Federal da Paraiba, Brazil, Didier Sornette, ETH Zurich, and Daniel Gauthier, Duke University, provide further quantitative support for the theories of Sornette (search) and colleagues that warning signs of impending catastrophic calamities can in fact be limned from hyper-complexities such as climates and economies, contrary to many denials. These significance insights are also well explained by mathematician James Weatherall in his fine The Physics of Wall Street: A Brief History of Predicting the Unpredictable (Houghton Mifflin Harcourt, 2013)

In many complex systems, large events are believed to follow power-law, scale-free probability distributions, so that the extreme, catastrophic events are unpredictable. Here, we study coupled chaotic oscillators that display extreme events. The mechanism responsible for the rare, largest events makes them distinct and their distribution deviates from a power-law. Based on this mechanism identification, we show that it is possible to forecast in real time an impending extreme event. Once forecasted, we also show that extreme events can be suppressed by applying tiny perturbations to the system. (Abstract)

Cepelewicz, Jordana. The Quest to Decode the Mandelbrot Set, Math’s Famed Fractal. Quanta. January 27, 2024. A science reporter writew a luminous review about the whole history of such fractional theories from Benoit and his predecessors to their present state. Its focal occasion was a 2023 conference in Denmark to guide this now global project going forward. The article covers two main themes with vignettes of mathematicians who have spent lifetimes plumbing the endless depths of these equations. At the center are Misha Lyubich and Dima Dudko from SUNY Stony Brook whose years go back to Moscow, Ukraine and Belarus. We also meet Jeremy Kahn, Mitsuhiro Shishikura. Wolf Jung, Arnaud Chéritat of the University of Toulouse, Carsten Petersen of Roskilde University who chaired the meeting, Christophe Yoccoz, and more. The other half is a succinct tutorial all about fractal geometries with vivid graphs and images.

See, for example, MLC at Feigenbaum points by Dudko and Lyubich at arXiv:2309.02107 on universal renormalizations. I heard Benoit speak in the 1990s at Boston University. Afterwards I asked him if a hierarchy aspect might apply to fractals. He replied, rather archly, I have no use for that word. Of course he is right because these infinite iterations are not a linear ladder but nature’s organic, self-similarity as it springs from an essential genome-like code-script. (In my 2004 talk on the home page I mused that Thomas Aquinas’ “analog of proper proportion” phrase would be an apt description.) But as 2024 is taken over by incendiary conflicts, however might such mathematical geometries, as Galileo once advised, ever become actually realized and availed?

Use a computer to zoom in on the Mandelbrot set’s jagged boundary, and you’ll encounter seahorses, parades of elephants, spiral galaxies and neuron-like filaments. No matter how deep you explore, you’ll always see near-copies. That endless complexity was a core element of James Gleick’s 1987 book Chaos. The Mandelbrot set had become a symbol and represented the need for a new mathematical language, a better way to describe the fractal nature of the world. It illustrated how profound intricacy can emerge from the simplest of rules — much like life itself with relative order and disorder. (JC)

Chandler, Jerry and Gertrudis Van de Vijver, eds. Closure: Emergent Organizations and Their Dynamics. New York: New York Academy of Sciences. Volume 901, 2000. Many articles consider autopoietic processes with regard to their property of constantly forming, describing and "closing" their “biosemiotic” identity. This is a sign-based organic viability which pervades the natural realm as living systems refer to and enhance their own internal definition and individuality.

Changizi, Mark and Darren He. Four Correlates of Complex Behavioral Networks: Differentiation, Behavior, Connectivity, and Compartmentalization. Complexity. 10/6, 2005. A hierarchical universality of these features is reported across a wide range of phenomena such as nervous systems, organisms, social groups, economies, and ecosystems.

Chen, Yanguang. Zipf’s Law, l/f Noise, and Fractal Hierarchy. Chaos, Solitons, & Fractals. 45/1, 2012. As the extended Abstract conveys, a Peking University, College of Urban and Environmental Sciences, systems geographer contributes to the growing realizations of nature’s universally invariant, scalar repetition of the same structural and processual phenomena everywhere.

Fractals, 1/f noise, and Zipf’s laws are frequently observed within the natural living world as well as in social institutions, representing three signatures of complex systems. All these observations are associated with scaling laws and therefore have created much research interest in many diverse scientific circles. However, the inherent relationships between these scaling phenomena are not yet clear. In this paper, theoretical demonstration and mathematical experiments based on urban studies are employed to reveal the analogy between fractal patterns, 1/f spectra, and the Zipf distribution. First, the multifractal process empirically suggests the Zipf distribution. Second, a 1/f spectrum is mathematically identical to Zipf’s law. Third, both 1/f spectra and Zipf’s law can be converted into a self-similar hierarchy. Fourth, fractals, 1/f spectra, Zipf’s law can be rescaled with similar exponential laws and power laws. The self-similar hierarchy is a more general scaling method which can be used to unify different scaling phenomena and rules in both physical and social systems such as cities, rivers, earthquakes, fractals, 1/f noise, and rank-size distributions. The mathematical laws of this hierarchical structure can provide us with a holistic perspective of looking at complexity and complex systems. (Abstract)

Christensen, Kim and Nicholas Moloney. Complexity and Criticality. London: Imperial College Press, 2005. A technical work rooted in statistical mechanics that implies in part that self-organization in non-equilibrium systems may be a unifying concept for a emergent natural complexity.

For our purposes, complexity refers to the repeated application of simple rules in systems with many degrees of freedom that gives rise to emergent behavior not encoded in the rules themselves. (vii) Criticality refers to the behavior of extended systems at a phase transition where observables are scale free, that is, no characteristic scales exist for these observables. (vii) Criticality is therefore a cooperative feature emerging from the repeated application of the microscopic laws of a system of interacting ‘parts.’ (vii)

The science of complexity is highly interdisciplinary. It deals with dynamical systems composed of many interacting units, for example grains in granular media, rocks in the crust of the Earth, water droplets in the atmosphere, networks of organisms in biology or agents in economics, etc. (253)

Chua, Leon. Local Activity is the Origin of Complexity. International Journal of Bifurcation and Chaos. 15/11, 2005. Another example of growing efforts to identify a common complex system, but with dense mathematics it is hard to see how this feature can fit the bill. But the universality concept – that the same complex dynamics recurs everywhere throughout a nested nature –has long been the payoff.

Many scientists have struggled to uncover the elusive origin of “complexity,” and its many equivalent jargons, such as emergence, self-organization, synergetics, collective behaviors, nonequilibrium phenomena, etc…..The purpose of this paper is to show that all the jargons and issues cited above are mere manifestations of a new fundamental principle called local activity, which is mathematically precise and testable. (3435)

Chua, Leon, et al. A Nonlinear Dynamics Perspective of Wolfram’s New Kind of Science. Part V: Fractals Everywhere. International Journal of Bifurcation and Chaos. 15/12, 2005. The other four parts appeared over the last two years in this publication. A highly technical meditation on a “universal computation” by cellular automata and neural networks which manifests a self-similarity throughout an emergent world.

Cilliers, Paul. Difference, Identity, and Complexity. Philosophy Today. Spring, 2010. A synopsis of Cilliers and Rika Preiser’s edited work next in search of workable ways to understand nature’s self-organizing interplay of creative diversity and essential unity.

The argument in this essay is primarily one which resists an interpretation of deconstruction, and a post-structural understanding of difference, as an absolute free-play. Deconstruction acknowledges the inevitability of structure, and of its transformation. This “double movement” should be central when we think of institutions and organizations. (63)

Cilliers, Paul and Rika Preiser, eds. Complexity, Difference and Identity: An Ethical Perspective. Berlin: Springer, 2010. University of Stellenbosch, RSA, systems philosophers gather papers to address a troublesome issue in nonlinear studies – how to square a prolific spontaneity with an implied steady source. Its sections of Complexity, Difference, Identity, Ethics of Complexity, and Consequences strive toward a necessary reciprocity. See chapters by Cilliers and Collier herein, also Cilliers’ synopsis in Philosophy Today, (Spring 2010).

Corning, Peter. Nature’s Magic: Synergy in Evolution and the Fate of Humankind. Cambridge: Cambridge University Press, 2003. A consummate volume to convey this biologist’s thesis that cooperative effects between, for example, genes or individuals, are equally as important as the components themselves. The theory posits that when cooperation produces beneficial functional effects or synergies (some are not beneficial), these may be favored or selected (synergistic selection). This propensity then plays a causal role in the evolution of emergent complexity from the origin of life to human societies.

Corominas-Murtra, Bernat, et al. Hierarchy in Complex Systems. arXiv:1303.2503. A March 2013 posting by Corominas-Murtra and Ricard Sole, Universitat Pompeu Fabra, with Joaquin Goni and Carlos Rodgiguez-Caso, Indiana University, which is seen as confirming a half century later, Herbert Simon’s advocacy that regnant nature relies on hierarchical modularities for its robust maintanence. Indeed this 21st century Barcelona-Bloomington team can avail theoretical computations to develop 3D visualizations, which reveals an implicate source from which these nested, evolutionary structures arise. Ricard Sole acknowledges conversations in regard at the Santa Fe Institute with Douglas Erwin, Eric Smith, Geoffrey West and Murray Gell-Mann. See for example, Colm Ryan, et al. “Hierarchical Modularity and the Evolution of Genetic Interactomes across Species” in Molecular Cell (46/691, 2012) which also cites “general design principles” at work.

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